velocity, the radius vector shews P's velocity. The motion of P
is known as pure harmonic, and occurs often in natural science.
Transferring P's velocities to a distance base gives a semicircular
curve, but on a time base forms the curve of sines.
The Beam Engine linkage is shewn in Fig. 460, with
centrodes and polar curves. The lines A p, B w, being at right
angles to the direction of motion of P and W respectively, will, if
produced, give the virtual centre M. Then if B K be || to AP,
the triangles M P w and B K w are similar, and
vel. W ^ M w "
the polar curves being completed as before. The centrode curve
only reaches infinity on the side j, when A H, B w are parallel ;
the ends OE meeting at a very great but finite distance. The
polar curves are similar to those of the crank and connecting rod,
P having greater velocity than W at times. When in the form 3,
Fig. 449, the quadric chain has its virtual centres always at infinity,
and therefore P and W have like velocities. (SeeApp. II., p. 863.)
Point paths are often of more importance than forces, but
can always be obtained by drawing the links in successive
positions ; and the mechanical advantage of a complex system is the
product of the advantages of its parts. Taking now the power
transmitters in order,
(I.) Link work is suitable only for short distances, as in
the case of locomotive coupling rods, and is rather a modifier
than a transmitter. We shall take a few further examples.
The Stanhope Levers, Fig. 461, were applied by Lord
Stanhope to his printing press. Two plan views are given : at
first P and W have nearly equal velocities, but when they have
moved to the positions Px and W1? the latter has* no velocity, while
the former has yet the original motion.
P's vel. _ i j
This means that a very great pressure is exerted at W when the
paper and type are in contact. A polar curve for W's velocity
has been drawn in the right-hand diagram, considering P's velocity